Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1, (which is identical to a standard gamma distribution with α = 1), compute the following. (If necessary, round your answer to three decimal places.) (a) The expected time between two successive arrivals
(b) The standard deviation of the time between successive arrivals
(c) P(X ? 1)
(d) P(2 ? X ? 5)

(a)

(b)

(c)  P(X ≤ 1) = 0.6321

(d) P(2 ≤ X ≤ 5) = 0.1286

Step-by-step explanation:

From the given information; Let consider X to be the time between two successive arrivals at the drive-up window of a local bank.

However; If X is regarded as the exponential distribution with λ = 1 which is identical to a standard gamma distribution with ∝ = 1

The objective is to compute the following :

(a) The expected time between two successive arrivals is;

(b)  The standard deviation of the time between successive arrivals is;

(c)  P(X ≤ 1)

P(X ≤ 1) = 1 - e⁻¹

P(X ≤ 1) = 0.6321

(d) P(2 ≤ X ≤ 5)

P(2 ≤ X ≤ 5) = [1 -  e⁻⁵] - [1 - e⁻²]

P(2 ≤ X ≤ 5) = 0.9933 - 0.8647

P(2 ≤ X ≤ 5) = 0.1286

for a it would be 24 children.

for b i don't understand the question. is it saying for each individual person they pick 5 reds to 7 greens or is it the whole group. clarify and i hope this can you.

step-by-step explanation:

brandon has 4344 video games.  

step-by-step explanation

7373 - 2929 = 4344

pls let me know if it was correct